Question

If the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is?

• A. Always greater than the original fraction
• B. Always less than the original fraction
• C. Always equal to the original fraction
• D. None of the above

Answer 1

The correct option is A Always greater than the original fraction

If the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is always greater than the original fraction.

Let us understand and verify it with the help of couple of examples:

$\left(i\right)$ Let $\frac{1}{2}$ be an original fraction.

$\frac{1}{2}=0.5$

If the numerator and denominator are increased by $5$, the fraction becomes:

$\frac{1+5}{2+5}=\frac{5}{7}=0.71$

$\therefore$ $\frac{1}{2}<\frac{5}{7}$

$\left(ii\right)$ Let $\frac{7}{9}$ be an original fraction.

$\frac{7}{9}\approx 0.78$

If the numerator and denominator are increased by $1$, the fraction becomes:

$\frac{7+1}{9+1}=\frac{8}{10}=0.8$

$\therefore$ $\frac{7}{9}<\frac{8}{10}$

Hence, if the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is always greater than the original fraction.

Therefore, option A is correct.